Two rods of same length and areas of cross-section A1 and A2 have their ends maintained at same temperature. If K1 and K2 are their thermal conductivities, C1 and C2 are the specific heats of their material and ρ1,ρ2 their densities, then for the rate of flow by conduction through them to be equal:

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Two rods of same length and areas of cross-section A₁ and A₂ have their ends maintained at same temperature. If K₁ and K₂ are their thermal conductivities, C₁ and C₂are the specific heats of their material and $ρ_{1}, ρ_{2}$ their densities, then for the rate of flow by conduction through them to be equal:

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$\frac{A_{1}}{A_{2}} = \frac{K_{1}}{c_{1} ρ_{1}} \frac{c_{2} ρ_{2}}{K_{2}}$

$\frac{A_{1}}{A_{2}} = \frac{K_{1}}{K_{2}}$

$\frac{A_{1}}{A_{2}} = \frac{K_{1} c_{1} ρ_{1}}{K_{2} c_{2} ρ_{2}}$

$\frac{A_{1}}{A_{2}} = \frac{K_{2}}{K_{1}}$

answer is D.

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Detailed Solution

$\frac{∆ Q}{∆ t} = \frac{K_{1} A_{1} (T_{1} - T_{2})}{l} = \frac{K_{2} A_{2} (T_{1} - T_{2})}{l} \Rightarrow \frac{A_{1}}{A_{2}} = \frac{K_{2}}{K_{1}}$